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Axisymmetric Stokes flow solutions a...

Hansen, David Gordon.

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Axisymmetric Stokes flow solutions and bubble microstreaming.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Axisymmetric Stokes flow solutions and bubble microstreaming./
Author:	Hansen, David Gordon.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2009,
Description:	233 p.
Notes:	Source: Dissertations Abstracts International, Volume: 70-12, Section: B.
Contained By:	Dissertations Abstracts International70-12B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3352551
ISBN:	9781109103717

Axisymmetric Stokes flow solutions and bubble microstreaming.
Hansen, David Gordon.

Axisymmetric Stokes flow solutions and bubble microstreaming. - Ann Arbor : ProQuest Dissertations & Theses, 2009 - 233 p.

Source: Dissertations Abstracts International, Volume: 70-12, Section: B.

Thesis (Ph.D.)--Northwestern University, 2009.

This item must not be sold to any third party vendors.

We analyze a large class of axisymmetric Stokes flows, in which the fluid is bounded below by a plane wall and driven locally by a compact object. In many such problems, the traditional solution method fails to satisfy the slip velocity at the plane. We prove that if a solution can be found to the axisymmetric Stokes problem with Dirichlet and Neumann boundary conditions, then it is unique, and we advance a novel Green's function method to find that solution. While these results are valid for any geometry, we derive the specific Green's function and resulting streamfunction solution for a hemispherical geometry above the plane wall. The elusive slip velocity is satisfied by an eigenfunction expansion exhibiting the Gibbs phenomenon, which we demonstrate can be largely eliminated using well-known methods. The resulting solution resolves a fifty-year-old problem that models a wide variety of applications. We use the above formalism to model the streaming flow from an oscillating microbubble attached to a plane wall. We solve the vorticity equation inside the bubble boundary layer and perform asymptotic matching to determine the coefficients of the far-field Stokes flow solution. We compare the analytical results to recent and classical experiments and find that our solution accounts for a flow reversal phenomenon related to the presence or absence of surfactant at the bubble interface. A method of image singularities is applied to find the streaming flow around a bubble between two parallel plane walls; we find that the circulation speed is increased in this case. We analyze transport and mixing applications of bubble streaming in the two-wall geometry and evaluate their efficacy.

ISBN: 9781109103717Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Bubble microstreaming

Axisymmetric Stokes flow solutions and bubble microstreaming.
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020 $a 9781109103717
035 $a (MiAaPQ)AAI3352551
035 $a (MiAaPQ)northwestern:10058
035 $a AAI3352551
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100 1 $a Hansen, David Gordon. $3 3548290
245 1 0 $a Axisymmetric Stokes flow solutions and bubble microstreaming.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2009
300 $a 233 p.
500 $a Source: Dissertations Abstracts International, Volume: 70-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Hilgenfeldt, Sascha.
502 $a Thesis (Ph.D.)--Northwestern University, 2009.
506 $a This item must not be sold to any third party vendors.
520 $a We analyze a large class of axisymmetric Stokes flows, in which the fluid is bounded below by a plane wall and driven locally by a compact object. In many such problems, the traditional solution method fails to satisfy the slip velocity at the plane. We prove that if a solution can be found to the axisymmetric Stokes problem with Dirichlet and Neumann boundary conditions, then it is unique, and we advance a novel Green's function method to find that solution. While these results are valid for any geometry, we derive the specific Green's function and resulting streamfunction solution for a hemispherical geometry above the plane wall. The elusive slip velocity is satisfied by an eigenfunction expansion exhibiting the Gibbs phenomenon, which we demonstrate can be largely eliminated using well-known methods. The resulting solution resolves a fifty-year-old problem that models a wide variety of applications. We use the above formalism to model the streaming flow from an oscillating microbubble attached to a plane wall. We solve the vorticity equation inside the bubble boundary layer and perform asymptotic matching to determine the coefficients of the far-field Stokes flow solution. We compare the analytical results to recent and classical experiments and find that our solution accounts for a flow reversal phenomenon related to the presence or absence of surfactant at the bubble interface. A method of image singularities is applied to find the streaming flow around a bubble between two parallel plane walls; we find that the circulation speed is increased in this case. We analyze transport and mixing applications of bubble streaming in the two-wall geometry and evaluate their efficacy.
590 $a School code: 0163.
650 4 $a Mathematics. $3 515831
650 4 $a Plasma physics. $3 3175417
653 $a Bubble microstreaming
653 $a Eigenfunction
653 $a Gibbs phenomenon
653 $a Green's function
653 $a Micromixing
653 $a Steady streaming
653 $a Stokes flow
690 $a 0405
690 $a 0759
710 2 $a Northwestern University. $b Applied Mathematics. $3 1023521
773 0 $t Dissertations Abstracts International $g 70-12B.
790 $a 0163
791 $a Ph.D.
792 $a 2009
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3352551